Endogenous entry and auctions design with private participation costs

Abstract

This paper studies endogenous entry and ex ante revenue-maximizing auctions in an independent private value setting where potential bidders have private-information entry costs. The contribution of this paper is four-fold. First, we show that any equilibrium entry can be characterized through a set of continuous and monotonic shutdown curves that separate the bidders' types into participating and nonparticipating categories. Second, the expected winning probability of a participant does not depend on his private entry cost. Furthermore, the expected winning probabilities of the participating types are given by the slopes of the shutdown curves. Third, symmetric entry equilibria (shutdown curves) implemented by the classes of ex post efficient or ex post revenue-maximizing mechanisms are completely characterized. Fourth, within these two classes of mechanisms, a modified Vickrey auction with uniform reserve price and entry subsidy is ex ante revenue-maximizing. The desired entry subsidy and reserve price are determined by the lower end of the corresponding shutdown curve.